# Interpretation of Johansen cointegration test in R

I am using urca package of R for Johansen Cointegration test in 2 stocks datas( A and B.

My question is very elementar, but have cause some problems for me. How I interpret the critical values, for exemple, H1 <- ca.jo(ll,type = "eigen", ecdet= "const", K = 4,spec = "longrun") produce:

Values of teststatistic and critical values of test:

test 10pct  5pct  1pct
r <= 1 |  6.39  7.52  9.24 12.97
r = 0  | 11.62 13.75 15.67 20.20

1 - In this case, for 10pct I have 11.62 < 13.75, then I can accept the hipotesis that A and B is not co-intregrate ? (whatever if for r <= 1 test is smaller that critical value ?).

2 - If for result in Trace statistic I find that A and B is cointegrate and for eigenvalue test A and B is not ? what does that mean it ? I reject the result of Trace Statistics in this case and admit A and Bnot cointegrate ?

• Hi @FlàvioCorinthians and welcome to quant.SE! Could you improve the question format? For instance, you could add the label to the test (c-value, p-value,..). Moreover, I suggest you to browse in quant.SE, since there are a lot of questions about cointegration test interpretation (see, for example, quant.stackexchange.com/questions/2076/…) Jul 13, 2015 at 9:54

## 1 Answer

Johansen test estimates the rank (r) of given matrix of time series with confidence level. In your example you have 2 time series, therefore Johansen tests null hypothesis of r=0 < (no cointegration at all), r<1 (till n-1, where n=2 in your example). If r<=1 test value (6.39) was greater than a confidence level's value (say 10%: 7.52), we would assume there is a cointegration of r time series (in this case r<=1). But as you see, none of your test values are greater than than critical values at r<0 and r<=1, therefore there is no cointegration.